- “… the movement an animal makes from its point of origin to the place where it reproduces or would have reproduced had it survived and found a mate.” – Howard 1960
March 21, 2022
Colonizers: pioneer new habitat patches as favorable patches wink out
Demographic buffers: reduce impact of mortality in prime-age individuals by providing a pool of ready replacements
Rescuers: provide new breeders or new genetics to isolated sub-populations that are declining.
Without disperal all metapopulations will eventually go extinct.
Alleles of Pgi gene in butterfly trade off metabolic rate (low = better disperser) with clutch size (Haag et al. 2005). Also, linked to probability of colonizing and heritability.
See: the loneliest California sea lion in the world (Zalophus californianus)
aggressive / less neophobic
But, agressive house mice Mus musculus domesticus drive away more timid mice (Pocock, Hauffe, & Searle, 2005)
Facial expressions of mice in aggressive and fearful contexts (Defensor 2012)
The act of disersal may make an animal bolder - example from Finnish wolves (Barry, Gurarie et al. 2020)
Ballochory (self seeder)
Zooballochory (impetus provided by animals) - Anemoballochory (impetus provided by wind) - Hydroballochory (impetus provided by water) - Autoballochory (propulsion mechanisms based on sap pressure or drying)
Ethelochory (deliberate dispersal) - Speirochory (dispersal due to accidental dispersal with seeds) - Agochory (unintentional dispersal)
A slowly widening bell-shaped curve
The 1-D probability of being in location \(x\) after time \(t\) given a random walk with diffusion constant \(D\) is:
Diffusion + colonization: \(\sqrt{Area} \propto t\)
Not \(Pr(x) \sim \exp(-x^2)\) but closer to \(Pr(x) \sim \exp(-x^\kappa)\) where \(0 < \kappa < 2\).
A fat-tailed model can actually lead to an accelerating invasion front!
(Skip to 8:45)
(Removed are either Recovered or Recently Deceased)
\[ \left\{\begin{aligned} & \frac{dS}{dt} = - \frac{\beta I S}{N}, \\[6pt] & \frac{dI}{dt} = \frac{\beta I S}{N}- \gamma I, \\[6pt] & \frac{dR}{dt} = \gamma I, \end{aligned}\right. \]
Note - the similarity (simplification) relative to predator-prey models. How many parameters are there?
Note - the sum of the three rates \({dS \over dt} + {dI \over dt} + {dR\over df} = 0\), because population is fixed at \(S+I+R = N\) (none of the crazy fluctuations of Lotka-Volterra).
Eventually EVERYONE will be Removed! (good news? bad news?)
SQUIRED model (should have been SQUIRREL)